Understanding how humans conceptualize and categorize natural objects offers critical insights into perception and cognition. With the advent of large language models (LLMs), a key question arises: can these models develop human-like object representations from linguistic and multimodal data? Here we combined behavioural and neuroimaging analyses to explore the relationship between object concept representations in LLMs and human cognition. We collected 4.7 million triplet judgements from LLMs and multimodal LLMs to derive low-dimensional embeddings that capture the similarity structure of 1,854 natural objects. The resulting 66-dimensional embeddings were stable, predictive and exhibited semantic clustering similar to human mental representations. Remarkably, the dimensions underlying these embeddings were interpretable, suggesting that LLMs and multimodal LLMs develop human-like conceptual representations of objects. Further analysis showed strong alignment between model embeddings and neural activity patterns in brain regions such as the extrastriate body area, parahippocampal place area, retrosplenial cortex and fusiform face area. This provides compelling evidence that the object representations in LLMs, although not identical to human ones, share fundamental similarities that reflect key aspects of human conceptual knowledge. Our findings advance the understanding of machine intelligence and inform the development of more human-like artificial cognitive systems. Multimodal large language models are shown to develop object concept representations similar to those of humans. These representations closely align with neural activity in brain regions involved in object recognition, revealing similarities between artificial intelligence and human cognition.